Controllable bright and dark rogue waves in inhomogeneous erbium doped fibers

• We discover rogue waves for a generalized nonlinear Schrödinger–Maxwell–Bloch model.
• We reduce the nonautonomous dynamical system to autonomous one.
• We also discuss the dynamical behavior of these rogue waves.

We report bright and dark rogue waves for a generalized nonlinear Schrödinger–Maxwell–Bloch model which describes the wave propagation in an inhomogeneous erbium doped fiber. This is achieved by reducing the inhomogeneous dynamical system to homogeneous dynamical model under certain parametric conditions (integrable conditions). We discuss the recurrence and annihilation of controllable bright and dark rogue waves as they propagate through a periodically distributed fiber-amplifier system. Furthermore, we investigate the nonlinear tunneling of these rogue waves as they propagate through a dispersion barrier or well.